Transitioning from counting to multiplying to find area | 3rd grade | Khan Academy

This square is one square unit. So, what is the area of rectangle A? The first thing we're told is that each of these little squares equals one square unit, and then we're asked to find the area of rectangle A. Here's rectangle A, and area is the space that it covers. So how much space does rectangle A cover? How many square units does rectangle A cover?

One way to answer that would be to count how many square units it covers, except they've covered up our square units. So, one idea is we could draw them back. Say you covered them up; we'll draw them back in. So, go in like this, connect all these, and then we should be able to count our square units.

So we have one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve. Twelve square units! Rectangle A covers 12 square units, so it has an area of 12 square units. But this isn't the only way that we could have solved this. We could have also said, we could have also looked at this and said, okay, this top row is four square units long. One, two, three, four. It has a length of four units, so that means the top row will have one, two, three, four square units inside of it.

Then we could have looked over on the side over here and said, well, how many rows of four will there be? There will be one, two, three rows of four. So we'll have this row of four, and then a second row of four, and a third. So, three times we will have four square units.

There's four square units at the top, another in the middle, and another at the bottom. Three times, we will have four square units. Or we could go even farther than that. We could have said we could have done three times four, or we could look at this and say, okay, here's one column. This column has three square units; it has a length of three. One, two, three.

How many of these columns like this will there be? There will be one, two, three, four, because our length here, but the top is four. So this time four times, we will see three square units—one, two, three—and we'll see that one, two, three, four times.

So no matter which of these we solved, whether we counted the square units like in the beginning or we multiplied the side lengths, the three and the four, in every case we're going to find that this equals 12 square units. The area of rectangle A is 12 square units because it covers 12 square units.